curve #3277

y² + xy = x³ − 41x + 96

a-invariants: [1, 0, 0, -41, 96]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 1095
discriminant (Δ): 147825
Faltings height: -0.2153
naive height: 22.7558
primes of bad reduction: 3, 5, 73
regulator: 1.150111900662175783653925541434844999869
submitted by: David Renshaw
submitted at: 2026-09-26 20:50:18 UTC
last updated: 2026-09-26 20:50:18 UTC

Witness: 1 independent point log in to add more points →

(3, 0)

Commentary

Cremona 1095a1 = LMFDB 1095.a3: https://www.lmfdb.org/EllipticCurve/Q/1095/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1095, minimal discriminant 147825, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:50:18 UTC · history